Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-9x-3y &= -1 \\ -7x+y &= -3\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-7x = -y-3$ Divide both sides by $-7$ to isolate $x$ $x = {\dfrac{1}{7}y + \dfrac{3}{7}}$ Substitute this expression for $x$ in the first equation. $-9({\dfrac{1}{7}y + \dfrac{3}{7}}) - 3y = -1$ $-\dfrac{9}{7}y - \dfrac{27}{7} - 3y = -1$ Simplify by combining terms, then solve for $y$ $-\dfrac{30}{7}y - \dfrac{27}{7} = -1$ $-\dfrac{30}{7}y = \dfrac{20}{7}$ $y = -\dfrac{2}{3}$ Substitute $-\dfrac{2}{3}$ for $y$ in the top equation. $-9x-3( -\dfrac{2}{3}) = -1$ $-9x+2 = -1$ $-9x = -3$ $x = \dfrac{1}{3}$ The solution is $\enspace x = \dfrac{1}{3}, \enspace y = -\dfrac{2}{3}$.